Alternate Interior - If two parallel lines are intersected by a transversal, then alternate interior angles are congruent.
Alternate Exterior - If two parallel lines are intersected by a transversal, then alternate exterior angles are congruent.
Parallel Lines Conjecture - If two parallel lines are intersected by a transversal, then corresponding angles, alternate exterior angles and alternate interior angles are congruent.
Converse of the Parallel Lines Conjecture- If corresponding angles, alternate exterior angles, or alternate interior angles are congruent, then two lines intersected by a transversal are parallel.
Perpendicular Bisector Conjecture - If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints.
Converse of the Perpendicular Bisector Conjecture - If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
Corresponding Angles - If two parallel lines are intersected by a transversal, then corresponding angles are congruent.
Linear Pair - If two angles form a linear pair, then the sum of their measures is 180 degrees (they are supplementary).
Vertical Angles - If two angles are vertical angles, then the angles are congruent. (measures are equal)
Shortest Distance Conjecture - The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line.
Obtuse Angle Conjecture - If an obtuse angle is bisected, then the resulting angles are acute.
Parallel Slope Property - If two lines are parallel, then their slopes must be equal (pg 167)
Perpendicular Slope Property - If a coordinate plane, two non-vertical lines are perpendicular if and only if their slopes are opposite reciprocals of each other. (pg 167)
Angle Bisector Concurrency Conjecture - The three bisectors of a triangle intersect to form the point called the incenter. (pg 178)
Perpendicular Bisector Concurrency Conjecture - The three perpendicular bisectors of a triangle intersect forming the circumcenter. (pg 179)
Altitude Concurrency Conjecture - The three altitudes (or the lines containing the altitudes) of a triangle intersect forming the orthocenter. (pg 179)
Circumcenter Conjecture - The circumcenter of a triangle is equidistant from the verticies of a triangle. (pg 179)
Incenter Conjecture - The incenter of a triangle is equidistant from the sides of the triangle. (pg 180)
Median Concurrency Conjecture - The three medians of a triangle intersect to form the centroid (pg 185)
Centroid Conjecture - The centroid of the triangle divides each median into two parts so that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side. (pg 186)
Center of Gravity Conjecture - The centroid of a triangle is the center of gravity of the triangular region. (pg 187)
Euler Line Conjecture - The circumcenter, centroid and orthocenter are the three points of concurrency that always lie on a line. (pg 191)
Euker Segment Conjecture - The centroid divides the Euler segment into two parts so that the smaller part is one half the larger part. (pg 192)
Triangle Sum Conjecture - The sum of the measures of the angles in every triangle is 180 degrees. (pg 201)
Third Angle Conjecture - If two angles of one triangle are equal in measure to two angles of another triangle, then the third angles of the triangles are congruent. (pg 204)
Triangle Inequality Conjecture - The sum of the lengths of any two sides of a triangle is greater than the length of the third side. (page 216)
Side-Angle Inequality Conjecture - In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side. (page 217)
SSS Congruence Conjecture: If 3 sides of 1 triangle are congruent to 3 sides of another triangle, then both the triangles are congruent
SAS Congruence Conjecture: If 2 sides and the included angle of 1 triangle are congruent to 2 sides and the included angle of another triangle, then both the triangles are congruent
ASA Congruence Conjecture: If 2 angles and the included side of 1 triangle are congruent to 2 angles and the included side of another, then the 2 triangles are congruen
AAS Congruence Conjecture: If 2 angles and a non-included side of 1 triangle are congruent to the corresponding 2 angles and non-included side of another triangle, then the 2 triangles are congruent
Corresponding Parts of Congruent Triangles (CPCTC): Corresponding parts of congruent triangles are congruent
Vertex Angle Bisector Conjecture: In an isosceles triangle, the bisector of the vertex angle is also the an altitude and a median
Equilateral/Equiangular Triangle Conjecture: Every equilateral triangle is equiangular, every equiangular triangle is equilateral
Biconditional - Both the statement and its converse are true
"Conjecture A" (page 246) - The bisector of the vertex angle is an isosceles triangle divides the isosceles triangle into two congruent triangles
"Conjecture B" (page 246) - The bisector of the vertex angle in an isosceles triangle is also the altitude to the base
"Conjecture C" (page 247) - The bisector of the vertex angle is an isosceles triangle is also the median to the base.
Rhombus Diagonals Conjecture - The diagonals of a rhombus are perpendicular and they bisect each other
Rhombus Angles Conjecture - The diagonals of a rhombus bisect the angles of the rhombus
Rectangle Diagonals Conjecture - The diagonals of a rectangle are congruent and they bisect each other
Square Diagonals Conjecture - The diagonals of a square are congruent, perpendicular, they bisect each other, and they bisect the angles of the square
Quadrilateral Sum Conjecture - The sum of the four interior angles of any quadrilateral is 360
Exterior Angle Conjecture – for any polygon, the sum of the measures of a set of exterior angles is 360.
Kite Angles Conjecture – the nonvertex angles of a kite are congruent.
Kite Diagonals Conjecture – the diagonals of a kite are perpendicular (is that right?)
Isosceles Trapezoid Conjecture - the base angles of a trapezoid are congruent
Three Midsegments Conjecture - the 3 midsegments of a triangle divide into 3 congruent triangles
Triangle Midsegment Conjecture – a midsegment of a triangle is parallel to the third side and half the length of the third side.
Trapezoid Midsegment Conjecture – the midsegment of a trapezoid is parallel to the bases and is equal in length to the average of the two bases
Parallelogram Opposite Angles Conjecture – the opposite angles of a parallelogram are congruent
Parallelogram Consecutive Angles Conjecture – the consecutive angles of a parallelogram are supplementary
Parallelogram Opposite Sides Conjecture – the opposite sides of a parallelogram are congruent and parallel
Parallelogram Diagonals Conjecture – the diagonals of a parallelogram bisect each other
Conjectures
Alternate Interior - If two parallel lines are intersected by a transversal, then alternate interior angles are congruent.
Alternate Exterior - If two parallel lines are intersected by a transversal, then alternate exterior angles are congruent.
Parallel Lines Conjecture - If two parallel lines are intersected by a transversal, then corresponding angles, alternate exterior angles and alternate interior angles are congruent.
Converse of the Parallel Lines Conjecture- If corresponding angles, alternate exterior angles, or alternate interior angles are congruent, then two lines intersected by a transversal are parallel.
Perpendicular Bisector Conjecture - If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints.
Converse of the Perpendicular Bisector Conjecture - If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
Corresponding Angles - If two parallel lines are intersected by a transversal, then corresponding angles are congruent.
Linear Pair - If two angles form a linear pair, then the sum of their measures is 180 degrees (they are supplementary).
Vertical Angles - If two angles are vertical angles, then the angles are congruent. (measures are equal)
Shortest Distance Conjecture - The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line.
Obtuse Angle Conjecture - If an obtuse angle is bisected, then the resulting angles are acute.
Parallel Slope Property - If two lines are parallel, then their slopes must be equal (pg 167)
Perpendicular Slope Property - If a coordinate plane, two non-vertical lines are perpendicular if and only if their slopes are opposite reciprocals of each other. (pg 167)
Angle Bisector Concurrency Conjecture - The three bisectors of a triangle intersect to form the point called the incenter. (pg 178)
Perpendicular Bisector Concurrency Conjecture - The three perpendicular bisectors of a triangle intersect forming the circumcenter. (pg 179)
Altitude Concurrency Conjecture - The three altitudes (or the lines containing the altitudes) of a triangle intersect forming the orthocenter. (pg 179)
Circumcenter Conjecture - The circumcenter of a triangle is equidistant from the verticies of a triangle. (pg 179)
Incenter Conjecture - The incenter of a triangle is equidistant from the sides of the triangle. (pg 180)
Median Concurrency Conjecture - The three medians of a triangle intersect to form the centroid (pg 185)
Centroid Conjecture - The centroid of the triangle divides each median into two parts so that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side. (pg 186)
Center of Gravity Conjecture - The centroid of a triangle is the center of gravity of the triangular region. (pg 187)
Euler Line Conjecture - The circumcenter, centroid and orthocenter are the three points of concurrency that always lie on a line. (pg 191)
Euker Segment Conjecture - The centroid divides the Euler segment into two parts so that the smaller part is one half the larger part. (pg 192)
Triangle Sum Conjecture - The sum of the measures of the angles in every triangle is 180 degrees. (pg 201)
Third Angle Conjecture - If two angles of one triangle are equal in measure to two angles of another triangle, then the third angles of the triangles are congruent. (pg 204)
Triangle Inequality Conjecture - The sum of the lengths of any two sides of a triangle is greater than the length of the third side. (page 216)
Side-Angle Inequality Conjecture - In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side. (page 217)
SSS Congruence Conjecture: If 3 sides of 1 triangle are congruent to 3 sides of another triangle, then both the triangles are congruent
SAS Congruence Conjecture: If 2 sides and the included angle of 1 triangle are congruent to 2 sides and the included angle of another triangle, then both the triangles are congruent
ASA Congruence Conjecture: If 2 angles and the included side of 1 triangle are congruent to 2 angles and the included side of another, then the 2 triangles are congruen
AAS Congruence Conjecture: If 2 angles and a non-included side of 1 triangle are congruent to the corresponding 2 angles and non-included side of another triangle, then the 2 triangles are congruent
Corresponding Parts of Congruent Triangles (CPCTC): Corresponding parts of congruent triangles are congruent
Vertex Angle Bisector Conjecture: In an isosceles triangle, the bisector of the vertex angle is also the an altitude and a median
Equilateral/Equiangular Triangle Conjecture: Every equilateral triangle is equiangular, every equiangular triangle is equilateral
Biconditional - Both the statement and its converse are true
"Conjecture A" (page 246) - The bisector of the vertex angle is an isosceles triangle divides the isosceles triangle into two congruent triangles
"Conjecture B" (page 246) - The bisector of the vertex angle in an isosceles triangle is also the altitude to the base
"Conjecture C" (page 247) - The bisector of the vertex angle is an isosceles triangle is also the median to the base.
Rhombus Diagonals Conjecture - The diagonals of a rhombus are perpendicular and they bisect each other
Rhombus Angles Conjecture - The diagonals of a rhombus bisect the angles of the rhombus
Rectangle Diagonals Conjecture - The diagonals of a rectangle are congruent and they bisect each other
Square Diagonals Conjecture - The diagonals of a square are congruent, perpendicular, they bisect each other, and they bisect the angles of the square
Quadrilateral Sum Conjecture - The sum of the four interior angles of any quadrilateral is 360
Exterior Angle Conjecture – for any polygon, the sum of the measures of a set of exterior angles is 360.
Kite Angles Conjecture – the nonvertex angles of a kite are congruent.
Kite Diagonals Conjecture – the diagonals of a kite are perpendicular (is that right?)
Isosceles Trapezoid Conjecture - the base angles of a trapezoid are congruent
Three Midsegments Conjecture - the 3 midsegments of a triangle divide into 3 congruent triangles
Triangle Midsegment Conjecture – a midsegment of a triangle is parallel to the third side and half the length of the third side.
Trapezoid Midsegment Conjecture – the midsegment of a trapezoid is parallel to the bases and is equal in length to the average of the two bases
Parallelogram Opposite Angles Conjecture – the opposite angles of a parallelogram are congruent
Parallelogram Consecutive Angles Conjecture – the consecutive angles of a parallelogram are supplementary
Parallelogram Opposite Sides Conjecture – the opposite sides of a parallelogram are congruent and parallel
Parallelogram Diagonals Conjecture – the diagonals of a parallelogram bisect each other